Integrability of the lattice potential Korteweg-de Vries equation.
by
Samuel Butler
University of Sydney
Coauthors: Nalini Joshi

The Korteweg-de Vries (KdV) equation is a well-known partial differential equation that has a variety of physical applications and possesses a rich class of soliton solutions which can be obtained through an inverse scattering transform. An interesting property of the KdV equation is that it is amenable to a family of transformations known as Backlund transformations, which result in iterations within the solution space. Demanding permutability of such transformations leads to an entirely new equation known as the lattice potential KdV equation, which is discrete in both independent variables. This talk will discuss the stunning integrability properties and soliton solutions of this partial difference equation, and the close resemblance that it bears to its continuous counterpart.

Date received: January 5, 2010